Difference between revisions of "Bi-Conjugate Gradient Stabilized"
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# rnd = a random vector used to start the algorithm. | # rnd = a random vector used to start the algorithm. | ||
| + | '''NOTES:'''<br> | ||
| + | # The BICGStabM only guarantees the convergence of the linear system associated with the pfncMatMult you give it. You need to check this in your code. In fact, you should have a segment of your code check for this. If one or more shifts fails, for example, you could restart them using a single shift inverter. They should converge quickly since they probably already have almost converged to the desired accuracy. | ||
*[[Example]] | *[[Example]] | ||
Revision as of 15:42, 21 April 2010
The bi-conjugate gradient stabilized method (BICGStab), returns the solution to a set of shifted linear systems of the form
\((M+\sigma_i) \textbf{x} =\textbf{b} \quad i=1,2,... ,N \)
where \( \sigma_i\) are the shift values.
Definitions:
\( \text{residue} = || ( M+\sigma_i) - \textbf{b} || \)
\( \text{error} = || ( M+\sigma_i) - \textbf{b} || / ||\textbf{b}|| \)
Usage
int qcd::bicgstabm_device(device_wilson_field &src, int noshifts, double shifts[],device_wilson_field* sol[], double dError, int maxiters, matmult<device_wilson_field>& pfncMatMult, device_random_field& rnd);
- src = b.
- noShifts = (N-1) the number of shifts minus one.
- shifts[] = a pointer to all shift values except the most singular value
- sol = a pointer to an array of N pointers pointing to the solutions.
- dError = the maximum error in the solution (see definition).
- maxiters = the maximum number of iterations allowed.
- pfncMatMult = pointer to the matrix multiplication.
- rnd = a random vector used to start the algorithm.
NOTES:
- The BICGStabM only guarantees the convergence of the linear system associated with the pfncMatMult you give it. You need to check this in your code. In fact, you should have a segment of your code check for this. If one or more shifts fails, for example, you could restart them using a single shift inverter. They should converge quickly since they probably already have almost converged to the desired accuracy.
